Determine mathematically, the minimum total cost of pollution reduction in a general case. Let the costs of reduction for each firm have the form C = f(y), whereyis the amount of reduction andfis any monotonically increasing function; this function is, however, different for each firm. LetTbe the total amount of pollution to be reduced (which is a constant), andtthe amount reduced by Firm 1 (which is a variable). The total cost is then

Ctot = C1 + C2 = f1(t) + f2(T-t)

Using calculus, what is the minimum value of Ctot, expressed in terms of these functions?